论文标题
从复杂网络上的光纤束模型中级联故障的本地化到平均现场行为的过渡
Transition from localized to mean field behaviour of cascading failures in the fiber bundle model on complex networks
论文作者
论文摘要
我们研究了纤维束在复杂网络上的失败过程，这些网络着重于纤维强度程度对从局部野外行为的过渡程度的影响。从常规的平方晶格开始，我们应用Watts-Strogatz重新布线技术在负载传输网络中引入远距离随机连接，并分析捆绑包的最终强度以及故障大小级数的统计数据在重新布线概率逐渐增加时变化。我们的计算表明，网络节点的强度障碍程度对局部到平均场过渡具有重大影响。特别是，我们表明过渡以重新布线概率的有限值开始，随着无序程度的降低，该过渡概率转移到更高的值。过渡仅限于定义明确的疾病范围，因此存在节点强度的阈值障碍，而网络结构的随机化均未提供任何整体负载轴承能力，也没有提供系统的级联耐受性。在低强度障碍下，完全随机的网络是最稳定的网络，而在较低的结构随机性下，最佳级联耐受性是最佳的。基于网络结构和强度障碍的相互作用，我们构建了一个分析论点，该论点提供了对数值发现的合理描述。
We study the failure process of fiber bundles on complex networks focusing on the effect of the degree of disorder of fibers' strength on the transition from localized to mean field behaviour. Starting from a regular square lattice we apply the Watts-Strogatz rewiring technique to introduce long range random connections in the load transmission network and analyze how the ultimate strength of the bundle and the statistics of the size of failure cascades change when the rewiring probability is gradually increased. Our calculations revealed that the degree of strength disorder of nodes of the network has a substantial effect on the localized to mean field transition. In particular, we show that the transition sets on at a finite value of the rewiring probability, which shifts to higher values as the degree of disorder is reduced. The transition is limited to a well defined range of disorder, so that there exists a threshold disorder of nodes' strength below which the randomization of the network structure does not provide any improvement neither of the overall load bearing capacity nor of the cascade tolerance of the system. At low strength disorder the fully random network is the most stable one, while at high disorder best cascade tolerance is obtained at a lower structural randomness. Based on the interplay of the network structure and strength disorder we construct an analytical argument which provides a reasonable description of the numerical findings.
